Space Charge Effects on Ion Mobility Spectrometry

We study the space charge limited maximal current density j″ of mobility-selected ions that can be transmitted in ion mobility spectrometry (IMS). Theory and experiments focus on differential mobility analyzers (DMAs), but are readily generalizable to other IMS devices. Repulsion between the ions in the cloud leads to beam spreading, with significant broadening once the ion number density n becomes comparable to the space charge saturation limit n_sat = ε_oE_o/(eΔ). Δ is the distance traversed by the ions in the direction of an externally imposed electric field E_o, and e is the charge on each ion. For ions of electrical mobility Z, j″ is then limited below j″_sat = ZE_oen_sat = Zε_oE_o²/Δ. A theory including diffusion and space charge effects is developed that reduces to Burgers' exactly solvable equation. The theory is tested in experiments with room temperature electrosprays (ES) of 100 mM [ethyl₃N⁺-formate^-] in methanol. This spray produces primarily a single ionic species at very high initial concentration n, which may be tuned above or below n_sat by varying the distance from the ES emitter to the inlet slit of the DMA. Mobility-selected ion densities n > 3.10⁸ ions/cm³ are achieved, with n~n_sat, and with drastically broadened mobility peak shapes having the approximate top hat-predicted shapes. However, the largest n values approaching n_sat are not quantitatively measurable because the densest sprays do not fill the outlet slit length. Graphical Abstract .